As described in Refs. [1]}, [2]}, numerical solutions to this equation can be straight-forwardly obtained once the EOMs for \(\psi \)  and \(\phi \)  have been solved. The resulting numerical conductivity \(\sigma \)  then displays the expected behaviour, as it can be observed in Fig. REF , where its real and imaginary parts are represented in red. In particular, its real part is negligible for smaller frequencies \(\omega <\omega _p\)  and becomes asymptotically unity as the frequency surpasses \(\omega _p\) , shaping the aforementioned gap around that frequency.
